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**Marcello Tobia Benvenuto**

MASTER DEGREE DISSERTATION IN MECHANICAL, AERONAUTICAL ENGINEERING Development of an automatic shape optimization platform for a laminar profile March - September 2013 Relatori : Prof. Jan Pralits Ing. Thomas Michon Studente : Marcello Tobia Benvenuto 21/03/2014 1 1 1 1

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**single turboprop aircraft:**

Introduction Daher Socata produces the world’s fastest single turboprop aircraft: TBM 850. As each aeronautic company, Reduce the consumption it works every day to improve the aircraft performance Increase the max. speed Reduce the drag on the surfaces: WING Fluid mechanics 21/03/2014 2 2 2 2

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**A thin layer arises close to the shape, called boundary layer.**

Physical phenomenon When a body is in motion in a flow, the flow adhere to it because of the viscosity. A thin layer arises close to the shape, called boundary layer. 21/03/2014 3 3 3 3

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**Laminar boundary layer: Turbulent boundary layer:**

Physical phenomenon External disturbances can enter the boundary layer and generate a turbulent flow through a Transition process. Skin Friction X/C Laminar boundary layer: Thin with regular streamlines; low skin friction. Turbulent boundary layer: Thick with irregular fluctuations; high skin friction. The transition phenomenon is very sensitive to the shape variations 21/03/2014 4 4 4 4

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Objective Reduce the friction drag on an airfoil by keeping the flow laminar over the largest possible portion of the surface. Automatic Shape Optimization Advantages: 1) Save time during a process 2) Run multiple repetitive simulations 3) Analyze automatically the good results, finding the optimum 21/03/2014 5 5 5 5

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**Contents Optimization platform for 2D Geometry**

2D optimization High and High/Low speed - results - discussion Creation wing Conclusions Future works 21/03/2014 6 6 6 6

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**Why a 2D geometry? The wing’s behaviors are given by its profiles.**

Relative Thickness: 16% Chord: m 21/03/2014 7 7 7 7

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**Optimization steps and tools**

Create the 2D geometry Catia V 5 Create the domain and the mesh ANSYS: Design Modeler and Mesh Optimization platform Flow Solver ANSYS: Fluent Boundary layer and its stability bl3D and Nolot code Mode Frontier 21/03/2014 8 8 8 8

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**Optimization steps and tools**

Create the 2D geometry Catia V 5 Create the domain and the mesh ANSYS: Design Modeler and Mesh Optimization platform Flow Solver ANSYS: Fluent Boundary layer and its stability bl3D and Nolot code Mode Frontier 21/03/2014 9 9 9 9

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Create the 2D geometry To limit the number of the geometric design variables Describing the shape with a small set of inputs 9 Polynomial approximations of curves CAD Software: Catia V 5 21/03/2014 10 10 10 10

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**Create the 2D geometry Constraints Design Parameters**

Radius of the circle Chord = 1 meter Position of point 2 and 9 inside square Thickness at 25% and 75% of the chord fixed. Tension of points 2,3,8,9 Thickness of trailing edge 21/03/2014 11 11 11 11

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**Optimization steps and tools**

Create the 2D geometry Catia V 5 Create the domain and the mesh ANSYS: Design Modeler and Mesh Optimization platform Flow Solver ANSYS: Fluent Boundary layer and its stability bl3D and Nolot code Mode Frontier 21/03/2014 12 12 12 12

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**Create the domain and the mesh**

Different domains and meshes have been investigated to find the best grid in terms of time and quality O-type domain Radius = 90 meters Grid close to the profile: Grid Profile 21/03/2014 13 13 13 13

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**Optimization steps and tools**

Create the 2D geometry Catia V 5 Create the domain and the mesh ANSYS: Design Modeler and Mesh Optimization platform Flow Solver ANSYS: Fluent Boundary layer and its stability bl3D and Nolot code Mode Frontier 21/03/2014 14 14 14 14

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**Key point for the stability analysis**

Flow solver Numerical solution of the Navier-Stokes’s equations FLUENT Velocity and pressure distribution Pressure Coefficient distribution on the root airfoil of TBM 850. Cruise conditions. Key point for the stability analysis Cp X/C Smoothness Good quality 21/03/2014 15 15 15 15

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**Optimization steps and tools**

Create the 2D geometry Catia V 5 Create the domain and the mesh ANSYS: Design Modeler and Mesh Optimization platform Flow Solver ANSYS: Fluent Boundary layer and its stability bl3D and Nolot code Mode Frontier 21/03/2014 16 16 16 16

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**Boundary layer and its stability: bl3D**

It calculates the parameters of the boundary layer from the Cp distribution bl3D code Laminar Boundary Layer's Equations 21/03/2014 17 17 17 17

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**Streamwise Wave number**

Boundary layer and its stability: NOLOT NOLOT is based on the Linear Stability: Flow decomposed in mean flow and unsteady disturbances u = U + u' The unsteady disturbance is represented by a wave with infinitesimal amplitude Frequency Streamwise Wave number Spanmwise Wave number 21/03/2014 18 18 18 18

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**Boundary layer and its stability: NOLOT**

Semi-empirical eN method Mack’s Law: N factor Turbulence intensity N = – 2.4 ln(Ti) < Ti < 21/03/2014 19 19 19 19

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**Objective functions To maximize the position of transition**

A change of the shape of a profile can lead to different value of Cl and Cm Changes of global repartition of lift Stability problems Stalling problems To minimize ∆Cl = |Cl – ClTBM| To minimize ∆Cm = |Cm – CmTBM| 21/03/2014 20 20 20 20

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**Optimization steps and tools**

Create the 2D geometry Catia V 5 Create the domain and the mesh ANSYS: Design Modeler and Mesh Optimization platform Flow Solver ANSYS: Fluent Boundary layer and its stability bl3D and Nolot code Mode Frontier 21/03/2014 21 21 21 21

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**Optimization platform: Mode Frontier**

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**Optimization platform: Mode Frontier**

Lift and Mom. coeff ∆Cl ∆Cm 21/03/2014 23 23 23 23

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**Contents Optimization platform for 2D Geometry**

2D optimization High and High/Low speed - results - discussion Creation wing Conclusions Future works 21/03/2014 24 24 24 24

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**Optimization 2D High speed**

high speed (cruise): M=0.51; h=26000 feet; aoa=0 degrees Strategy optimization - explore all the domain of input parameters DOE - optimize the best profiles found by DOE with genetic algorithm 21/03/2014 25 25 25 25

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**TBM (trans. 26% of the chord)**

Pareto front opt. 2D high speed 399 profiles have been explored in 8 days Max ∆Cl 3% ∆Cl Max trans. 47% of the chord TBM (trans. 26% of the chord) Transition location 21/03/2014 26 26 26 26

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**Best solution opt. 2D high speed**

BLACK = TBM RED = BEST 21/03/2014 27 27 27 27

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**c A big influence of the leading edge on the transition**

Robustness solution for manufacturing? 0.07% of 1765 mm = 1.19 mm c A big influence of the leading edge on the transition Solution not robust 21/03/2014 28 28 28 28

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**Drag evaluation with transition model**

To evaluate the difference of drag, the SST-transition model is used in Fluent to study the natural transition: 21/03/2014 29 29 29 29

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**Optimization 2D High/Low speed**

To analyze stall characteristics at low speed, the profile has been optimized also at take-off conditions - High speed (cruise): M=0.51; h=26000 feet; aoa=0 degrees - Low speed (take-off): M=0.18; h=0; aoa= > 15 degrees 21/03/2014 30 30 30 30

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**Objective functions Cruise condition:**

To maximize the transition location To minimize ∆Cl and ∆Cm Take-off condition: Maximize the max Lift coefficient 21/03/2014 31 31 31 31

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**Pareto front 2D opt. High/low speed**

Cl low speed Transition high speed The objective functions are in opposition one with the other The same optimization has been done for the tip profile of the wing 21/03/2014 32 32 32 32

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**Discussion optimization 2D**

High speed Big sensibility of the phenomenon by the shape variations Transition moved from 26% to 47% of the chord Viscous drag reduced of 14.26% Improvements limited by the constraints of the shape: transition occurs close to the maximum thickness High/low speed Each flight condition requires a different optimal shape The presence of a new O.F. has not penalized the transition (42%) Improvements limited by the constraints of the shape 21/03/2014 33 33 33 33

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**Contents Optimization platform for 2D Geometry**

2D optimization High and High/Low speed - results - discussion Creation wing Conclusions Future works 21/03/2014 34 34 34 34

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Creation wing Creation of a wing with the optimal root and tip profile obtained previously Wing parameters: The same of the wing of TBM 850 - span: mm - dihedral: 6.5 degree 21/03/2014 35 35 35 35

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CFD Simulation 3D To compare the wing of the TBM 850 with the wing using the optimal profiles. TBM NEW Skin Friction 21/03/2014 36 36 36 36

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**Skin friction on profile at 50% of the span**

Results 3D Wing Visc. drag Press. drag Total drag Lift coeff TBM 0.1919 New 0.1903 New Skin Friction TBM Chord Skin friction on profile at 50% of the span 21/03/2014 37 37 37 37

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Discussion The validation on the wing has given unexpected results in terms of drag: The effects of the flows on 2D and 3D geometry are different - trailing vortex - cross flow disturbances X - Wall shear stress 21/03/2014 38 38 38 38

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Discussion The validation on the wing has given unexpected results in terms of drag: The effects of the flows on 2D and 3D geometry are different - trailing vortex - cross flow disturbances 21/03/2014 39 39 39 39

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**Contents Optimization platform for 2D Geometry**

2D optimization High and High/Low speed - results - discussion Creation wing Conclusions Future works 21/03/2014 40 40 40 40

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Conclusions I am familiar with software like Catia V 5, Fluent (2D and 3D), Fortran, Python, modeFRONTIER I created an automatic shape optimization for 2D geometry The strategy used, has allowed to obtain good results for 2D geometry - transition phenomenon delayed from 26% to 47% of the chord - Viscous drag reduced more than 14% 21/03/2014 41 41 41 41

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**Future work and suggestions**

Optimization 2D: New parameterization (CST) with other constraints can be tested More time for the iterations can lead a better results 3D Validation: To consider 3D effects we can run the following loop: Study the flow around the wing Take Cp distribution of three profiles of the wing (root, middle, tip) Run optimization platform for the three profiles To rebuild the wing with the three new profiles and study the flow on the wing 21/03/2014 42 42 42 42

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**Thank you for your attention**

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